Scribd
Upload
91 views4 pages

New Wordpad Document

The addition theorem of probability states that the probability of event A or event B occurring is equal to the probability of A occurring plus the probability of B occurring minus the probability of both A and B occurring. For mutually exclusive events, where A and B cannot both occur, the probability of both occurring is 0 and the formula reduces to the probability of A or B being the sum of the individual probabilities. The multiplication theorem states that the probability of events A and B both occurring is equal to the probability of A occurring multiplied by the conditional probability of B occurring given that A has occurred. For independent events that do not influence each other, the formula simplifies to the product of the individual probabilities of A and B occurring.

Uploaded by

Mahendra Bairwa
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as RTF, PDF, TXT or read online on Scribd
91 views4 pages

New Wordpad Document

The addition theorem of probability states that the probability of event A or event B occurring is equal to the probability of A occurring plus the probability of B occurring minus the probability of both A and B occurring. For mutually exclusive events, where A and B cannot both occur, the probability of both occurring is 0 and the formula reduces to the probability of A or B being the sum of the individual probabilities. The multiplication theorem states that the probability of events A and B both occurring is equal to the probability of A occurring multiplied by the conditional probability of B occurring given that A has occurred. For independent events that do not influence each other, the formula simplifies to the product of the individual probabilities of A and B occurring.

Uploaded by

Mahendra Bairwa
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as RTF, PDF, TXT or read online on Scribd
You are on page 1/ 4

Q.

State and illustrate Addition and Multiplication Theorem of probability.

Ans. Addition Theorem---A compound event is any event combining two or more simple events. The notation for addition rule is: P(A or B) = P(event A occurs or event B occurs or they both occur). When finding the probability that event A occurs or event B occurs, find the total numbers of ways A can occurs and the number of ways B can occurs, but find the total in such a way that no outcome is counted more than once. General addition rule is : P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) denotes that A and B both occur at the same time as an outcome in a trial procedure. It is a special addition rule that shows that A and B cannot both occur together, so P(A and B) becomes 0: If A and B are mutually exclusive, then P(A) or P(B)= P(A or B) = P(A) + P(B)

Addition Rule The addition rule is a result used to determine the probability that event A or event B occurs or both occur. The result is often written as follows, using set notation:

where: P(A) = probability that event A occurs P(B) = probability that event B occurs

= probability that event A or event B occurs

= probability that event A and event B both occur

For mutually exclusive events, that is events which cannot occur together:

=0 The addition rule therefore reduces to

= P(A) + P(B) For independent events, that is events which have no influence on each other:

The addition rule therefore reduces to

Example Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. We define the events A = 'draw a king' and B = 'draw a spade' Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have:

= 4/52 + 13/52 - 1/52 = 16/52

So, the probability of drawing either a king or a spade is 16/52 (= 4/13). See also multiplication rule.

Multiplication Rule The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. The result is often written as follows, using set notation:

where: P(A) = probability that event A occurs P(B) = probability that event B occurs

= probability that event A and event B occur P(A | B) = the conditional probability that event A occurs given that event B has occurred already P(B | A) = the conditional probability that event B occurs given that event A has occurred already For independent events, that is events which have no influence on one another, the rule simplifies to:

That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.

You might also like